1. 8087 instruction set and examples

2. About the 8087
In the old days, you had to buy a -87 chip for numerical co-processing and hand install it. (Back in the 8086, 286,386 days).
With the 486 processor and later, the -87 coprocessor is integrated.

3. About the 8087
The 8087 uses a “stack” or chain of 8 registers to use for internal storage and data manipulation, as well as status and control words to set rounding control and indicate the results of operations.
It has its own instruction set, instructions are recognizable because of the F- in front. (Like FIADD, FCOM, etc)

4. About the 8087
FWAIT… checks a control line to see if the 87 is still active.
programmers used to have to use an FWAIT before and after a set of instructions for the -87 to make sure -86 or -87 storage operations had been completed. (Basically, to handle synchronization).
FWAIT should not be necessary.

5. About the 8087: data transfer
Instruction result
FLD source load a real into st(0)
FST dest store real at dest (86 mem)
FSTP dest store/pop st(0)
FXCH {st(i)} exchange two regs (St(0), St(1)) or St(0) and the operand

6. About the 8087: data transfer
FILD source int load
FIST dest int store
FISTP dest int store/pop
FBLD source bcd load (tbyte source)
FBSTP dest bcd store tbyte dest

7. About the 8087: arithmetic FADD source add a real (mem) to st(0)
FADD {St(1),ST}
FADD st(i),st … or FADD ST,ST(i)
FADDP St(i),ST add st to st(i) and pop st(0)
FIADD {st,} source int add to st

8. About the 8087: arithmetic
FSUB for real subtract has same formats as FADD
FISUB {st,} intmem for int sub
ALSO:
FSUBR {st(1),st}
FSUBR {st,} rmem
FSUBRP st(i),st
Etc and …
FISUBR {st,} intmem
Reverse subtract: subtract dest from source

9. About the 8087: arithmetic FMUL and FIMUL have same formats available
FDIV and FIDIV have same formats
Also available
FDIVR, FDIVRP and FIDIVR

10. About the 8087: arithmetic Miscellaneous FSQRT {st} FABS {st}
FCHS {ST}… change sign
FLDZ {st}… load a zero

11. Control word
The control word is a 16 bit word that works like a flag register on the 86 processor. It keeps information about zerodivide in bit 2 for example. Bits 3 and 4 are overflow and underflow respectively.
Precision control is set in bits 8 and 9 and rounding is set in bits 10 and 11.
Rounding control bit settings are:
00 round to nearest/even
O1 round down
10 round up
11 chop/truncate

12. Status word Status word is also a 16 bit word value.
condition bits are named c3, c2,c1 and c0. Their position in the status word, though is:
C3 is bit 14
C2,c1,c0 are bits 10,9,8 respectively.
If you are curious, the eight possible bit settings in bits (11,12,13) indicate which register in the chain is currently st(0)

13. Temp real (80 bits)
Temp real has an f-p format. Bits are the significand in hidden bit format. Bits 64 to 78 are the biased exponent, bit 79 is the sign.
You shouldn’t need to worry about these values on the stack.

14. Packed bcd (80 bits) A packed bcd is a tbyte. Bit 79 is the sign.
Bits 72 through 78 are not used.
Bits 0,1,2,3 store the 0 th (lsd) decimal digit.
Bits 4,5,6,7 store the 1st.
The 17th (msd) digit is in bits 68,69,70,71.
You’ll need to pad with zeros if there are fewer than 18 digits.

15. Int values
87 processor recognizes word, dword and qword signed int types, in the same manner as the 86 processor.

16. The stack
Pushing and popping on the stack change the register who is currently the top.
Pushing more than 8 times will push the last piece of data out and put St(0) at the most recently pushed item.
It is the programmer’s responsibility to count stack push/pop operations.
Whoever is on top of the stack, is referenced by St or ST(0). St(1) is next. And so on to St(7).

17. Int transfer
FILD: load int. Type (word, dword, etc) is whatever the operand type is. St(0) is this new value. St(1) points to the previous value on top.
FIST: copy St(0) value to memory, converting to a signed int (following rounding control settings in the control word)
FISTP: same as above, but pop the stack as well.

18. BCD FBLD load a bcd (tbyte) onto the stack
FBSTP store a tbyte bcd value into the memory operand, popping the stack as you go.
Example:
FBLD myval
FBSTP myval

19. Exchanging/swapping on the stack
FXCHG dest
Swap stack top with operand.
Example
FXCHG St(3)
; swaps St(0) value with St(3) value

20. Int arithmetic FIADD, FIADD: add
FISUB, FISUBR, : sub, or sub reversed.
FIMUL
FIDIV, FIDIVR
Other:
FPREM, FRNDINT – partial remainder, round to int
FLDZ push a zero onto the stack.
FLD1 push a 1

21. FPREM Takes implicit operands st,st(1)
Does repeated subtract… leaves st>0,(possibly st==st(1)) or st==0.
May need to repeat it, because it only reduces st by exp(2,64)
If st>st(1) it needs to be repeated.
FPREM sets bit C2 of the status word if it needs to be repeated, clears this bit if it completes operation.

22. operands Stack operands may be implicitly referenced.
FIADD, FISUB, FIDIV, FIDIVR, FIMUL and FISUBR have only one form (example using add instruction):
FIADD {ST,} intmem
St(0) is implied dest for all of these.

23. comparison FCOM ;no operands compares st,st(1)
FCOM St(i); one operand compares st with st(i)
FCOMP (compare and pop) is the same.
FCOMPP - only allows implicit operands St,st(1) (compare then pop twice)
FTST – compares St with 0.
These all use condition codes described above and make the settings in the next slide.

24. Condition codes C3 c0 0 0 st>source 0 1 st<source 1 0 st==source
1 1 not comparable

25. Getting status and control words
FSTSW intmem ; copy status word to 16 bit mem location for examination.
FLDCW intmem; load control word (to set rounding, for example, from 16bit int mem)
FSTCW intmem; copy control word to int mem

26. Some -87 examples

27. 16-bit vs 32-bit? Almost all the examples here were done in 32 bit.
But the coprocessor works in 16 bit as well.

28. excerpt from a 16-bit program & ouptut
value word 1234
.code
main PROC
mov
mov ds,ax
mov ax, value
call writedec
fild value
fiadd value
fistp value
mov ax,value
call crlf
C:\MASM615>coprocessor
1234
2468
C:\MASM615>

29. adding up an array (example from notes)
include irvine16.inc
.data
array dword 12, 33, 44,55,77,88,99,101,202,9999,111
sum dword ?
.code
main proc
mov
mov ds,ax
xor bx,bx
fldz
fist sum
mov eax,sum;;;
call writeint;print zero
call crlf
mov cx,10
top:
mov eax,array[bx];;get value
call writeint;;;print it
fiadd array[bx];;;;add to st(0)
add bx,4
loop top
fistp sum;;;;when done pop to dword int
mov eax,sum
call writeInt;;;;print it
mov ax,4c00h
int 21h
main endp
end main

30. adding up an array (example from notes)

31. Getting sqrt call readint fstcw control;;;store current control word
or control,0800h;set bit 11 clear bit 10 to round up
fldcw control;;load new control word
mov num,eax
fild num
fsqrt
fistp sqr
fwait
mov edx, offset prompt2
call writestring
mov eax,sqr
call writeint

32. Rounding set to round up
c:\Masm615>primes
enter an integer125
sqrt of integer+12

33. Add code to check for prime and print divisors for composites
mov eax,num
call crlf
mov ebx,2;;;first divisor
top:
xor edx,edx
push eax
div ebx;;divide
mov divi,ebx
cmp edx,0
je notprime
inc ebx
cmp ebx,sqr
jg prime
pop eax
jmp top
notprime:
call writedec
mov eax,divi
mov edx,offset f
call writestring
prime:
mov edx,offset t

34. Output from primes enter an integer1337711 18841 71 not a prime
c:\Masm615>primes
enter an integer
746597 23
enter an integer313713
104571 3
enter an integer313717
prime
c:\Masm615>

35. factorials call readint mov num,eax call crlf
fld1 ;;load a 1 for subtacting and comparing..this will be st(2)
fld1 ;;prod value initialized in st(1)
fild num;;;multiplier... need to count down and multiply st by st(1)
theloop:
ftst ;;is st==0?
fstsw status
and status, 4100h;check bits c3 and c0...c3=0 c0=1 means st<source
cmp status,4000h;;st==source
jz done
fmul st(1),st ;;leave prod in st(1)
fsub st,st(2)
jmp theloop
done:
fistp dummy
fistp answer
mov edx,offset p2
call writestring
fwait
mov eax,answer
call writedec

36. factorials c:\Masm615>factorials enter an integer6 factorial is 720
5040
c:\Masm615>

37. Fibonacci values mov edx, offset prompt call crlf call writestring
call readint
fld1 ;;load a 1 for subtacting and comparing..this will be st(2)
fld1 ;;prod value initialized in st(1)
top: cmp eax,0
je done
fadd st(1),st
fsubr st,st(1) ;;;cute huhn?st=st(1)-st
dec eax
jmp top
done:
fistp dummy
fistp answer
mov edx,offset p2
fwait
mov eax,answer
call writedec

38. Fibonacci c:\Masm615>fibs enter an integer4 fib is 821
enter an integer7 34
c:\Masm615>

39. Mimicking real io
You can output reals by outputting first the integer part, subtracting this from the original value, then repeatedly multiplying the fraction by ten, (subtracting this off from the remainder) and outputting this sequence of fractional digits.
This is NOT an IEEE f-p conversion routine!

40. Rounding control & the int part
fstcw control
or control,0C00h ;;;chop or truncate
fldcw control
fild ten ;;ten is in st(1)
fild num ;;num is in st(0)
fsqrt ;;sqrt in st
fist intsqr ;;;store chopped result, don’t pop
call crlf
mov edx,offset message
call writestring
fwait
mov ax,intsqr ;;write the int part
call writedec

41. realio mov edx,offset dot;;decimal point call writestring
fisub intsqr ;;subtract from sqrt the int part leaving fractional part
;now loop & store 5 decimal places
mov edi, offset decimals
mov ecx, 5
up:
fmul st,st(1) ;;multiply by 10 to shift dec point
fist digit ;store truncated int
fisub digit ;;subtract it off of the total
fwait
mov ax,digit
add al,48
mov byte ptr [edi],al ;;store this digit
inc edi
loop up

42. Run of realio c:\Masm615>realio enter an integer: 121
sqrt of integer
123
sqrt of integer
143
sqrt of integer
c:\Masm615>